- Research Article
13
- 10.2139/ssrn.1012521
Analytic Approximations for Spread Options
- Sep 06, 2007
- SSRN Electronic Journal
- Carol Alexander + 1 more +1
Analytic Approximations for Spread Options
A story in Aristotle's Politics is often cited as the first published discussion of a financial derivative, an instrument whose value is derived from other assets or events. In Greece of the fifth century B.C., the philosopher Thales, believing six months in advance that the spring weather would be exceptionally favorable to olive growth, negotiated the right to rent oil presses for the next harvest at a bargain rate from press owners who wanted to hedge their bets against the possibility of a poor harvest. In today's parlance, Thales purchased a call option. When spring brought a lush olive harvest, Thales rented the machines to others at a much higher rate, making a tidy profit to support his philosophical inquiries. Options and other financial derivatives have become extremely popular in recent years, for better or worse. Overinvestment in derivatives of questionable value has led to notorious financial disasters such as the bankruptcy of Orange County, California, and the collapse of Barings Bank. Warren Buffett famously described derivatives as "financial weapons of mass destruction" in the Berkshire Hathaway Annual Report of 2002. Nonetheless, derivatives are undoubtedly here to stay; in 2002, trade in derivatives worldwide was estimated at $100 trillion or more, equaling or exceeding the total value of "real" equities. Readers of SIAM Review can take a special interest in derivatives because their analysis is an arena in which mathematics has had a huge impact on finance. In particular, the 1970s papers of Black and Scholes (1973) and Merton (1976) began a flood of research on options pricing that continues to this day. This issue's Survey and Review paper focuses on the special case of a spread option, a derivative that is based on the difference in value of two assets. Suppose you have some money to invest and the choice between two stocks to buy. You suspect that one will do much better than the other over the next few years, but you don't know which one. An ideal situation might be if you could buy one of them and hold it for a certain length of time, and then have the option of trading it in for the other stock if it turns out that that one did better. Another way to achieve the same benefit would be if someone agreed to pay you the difference in value between the two stocks at some specified time if you discover with hindsight that you made the wrong decision. Of course no one will offer you such an option free of charge, and so the mathematical question is how to price this option. This question is even more challenging if the option has a strike price that must be paid in order to exercise it. While spread options aren't publicly traded on arbitrary pairs of stocks, a variety of complex spread options are available in many markets, and are particularly popular in energy markets. Energy prices are extremely volatile compared to other commodities, a fact that most consumers are well aware of and that greatly affects producers, distributors, and speculators. Spread options are an important hedging and speculation tool, and are available in many different forms. For example, options may be based on the difference between the prices of two different forms of oil (the crack spread), between the prices of oil and electricity (the spark spread), or between the prices of a single commodity at two different times (calendar spreads) or locations (locational spreads). In the following article by Carmona and Durrleman, section 2 is devoted to a detailed description of these and other spread options that are used in practice. The authors then summarize the classical Black--Scholes pricing paradigm for options based on a single commodity, and the multivariate extensions needed for the analysis of spread options. The underlying stochastic differential equations can be solved by various approaches, and several approximations are illustrated and compared. Particular difficulties associated with energy markets are discussed throughout and are a main focus of the latter sections. Financial mathematics is as exciting growth area for applied mathematics, and we hope this paper will introduce readers to some challenging problems of current interest in this field.
Analytic Approximations for Spread Options
Analytic Approximations for Spread Options
Stochastic Correlation in Commodity Spread Options
Stochastic Correlation in Commodity Spread Options
An integrated electric power supply chain and fuel market network framework: Theoretical modeling with empirical analysis for New England
In this article, we develop a novel electric power supply chain network model with fuel supply markets that captures both the economic network transactions in energy supply markets and the physical network transmission constraints in the electric power network. The theoretical derivation and analysis are done using the theory of variational inequalities. We then apply the model to a specific case, the New England electric power supply chain, consisting of six states, five fuel types, 82 power generators, with a total of 573 generating units, and 10 demand market regions. The empirical case study demonstrates that the regional electric power prices simulated by our model match the actual electricity prices in New England very well. We also compute the electric power prices and the spark spread, an important measure of the power plant profitability, under natural gas and oil price variations. The empirical examples illustrate that in New England, the market/grid‐level fuel competition has become the major factor that affects the influence of the oil price on the natural gas price. Finally, we utilize the model to quantitatively investigate how changes in the demand for electricity influence the electric power and the fuel markets from a regional perspective.The theoretical model can be applied to other regions and multiple electricity markets under deregulation to quantify the interactions in electric power/energy supply chains and their effects on flows and prices. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009
Read moreThe spark spread and clean spark spread option based valuation of a power plant with multiple turbines
The spark spread and clean spark spread option based valuation of a power plant with multiple turbines
Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios
Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios
Analysis of the hedging strategy for the huge loss of Sinopec Group
The use of crude oil futures for hedging is common for companies that use crude oil as a raw material. It helps companies to hedge against the risks associated with the volatility of crude oil prices and avoid major problems such as cash flow shortages. However, if hedging is abused, it can also have a significant impact on a company's profits. In late 2018, one of Sinopec Group's subsidiaries, United Petrochemical, mistakenly used financial derivatives to hedge, resulting in a plunge in net profit and share price for the entire group. This article analyses Sinopec Group's financial position for the three years 2017, 2018, and 2019, examines United Petrochemical's hedging strategy, and ultimately points out the reasons for and implications of its failure, with a view to providing lessons for the subsequent use of financial derivatives for hedging in related industries. The authors found that a subsidiary of Sinopec Group incurred large losses when international crude oil prices fell as it bought too many futures, causing Sinopec Group's profits to fall by more than 90% in the fourth quarter of 2018 and evaporating more than RMB 90 billion in market value in the two days the deal came to light.
Read morePricing spark spread options in electricity markets
This master's thesis develops a pricing method for spark spread options using a Monte Carlo method. The underlying commodities of interest, natural gas and uranium highlight the prevalence of natural gas power and nuclear power in Canada. To characterize the dynamics of electricity prices and capture specific features they have, two Levy models are proposed: a jump-diffusion model and a time-changed model. Real data are used to calibrate the models, using the daily average market prices for the last five years. We created a method to compute the price of the derivative under realistic modelling conditions using parameters found through the real data. Such models can be used to value the spark spread contracts to mitigate the risk associated the contracts.
Read moreLévy-Based Cross-Commodity Models and Derivative Valuation
Energy commodities, such as oil, gas, and electricity, lack the liquidity of equity markets, have large costs associated with storage, exhibit high volatilities, and can have significant spikes in prices. Furthermore, and possibly more importantly, commodities tend to revert to long run equilibrium prices. Many complex commodity contingent claims exist in the markets, such as swing and interruptible options; however, the current method of valuation relies heavily on Monte Carlo simulations and tree-based methods. In this article, we develop a new cross-commodity modeling framework which accounts for jumps and cointegration in prices and introduce a new derivative valuation methodology by working in Fourier space. The method is based on the Fourier space time-stepping algorithm of Jackson, Jaimungal, and Surkov [J. Comput. Finance, 12 (2008), pp. 1–28] but is tailored for mean-reverting models. We demonstrate the utility of the method by applying it to European, American, and barrier options on a single commodity, to European and Bermudan spread options on two commodities, and to a particular class of swing options.
Read moreFactor affecting the Sino-Russian cooperation in energy trade
The research focuses on analyzing the development status, dynamic mechanisms, and optimization strategies of energy trade between China and Russia, combining theoretical analysis with empirical modeling. The study first reviews the theoretical basis of Sino-Russian energy trade, including the theory of comparative advantage and energy geopolitics, and systematically combs the historical evolution of energy trade in coal, oil, natural gas, and electricity. It is found that Chinas growing energy demand gap and Russias abundant energy reserves form a complementary foundation, while the "Ice Silk Road" initiative and the Russia-Ukraine conflict have significantly impacted trade patterns. Based on monthly data from 2016 to 2023, a VAR model is constructed to empirically test the impact of variables such as Sino-Russian GDP, energy consumption, production, and Brent crude oil prices. The results show that Russias GDP and international oil prices are the key factors, explaining 17.03% and 16.59% of trade volume fluctuations, respectively. Chinas economic growth and energy demand demonstrate short-term effects, while Russias energy production has a limited direct impact. Impulse response analysis reveals that rising oil prices initially suppress trade but later promote cooperation through long-term contract mechanisms. The research proposes five-dimensional policy recommendations: promoting local currency settlement and energy financial derivatives, deepening market reforms and price mechanism optimization, strengthening political trust and multilateral cooperation, advancing green energy collaboration and environmental supervision, and accelerating infrastructure construction such as Arctic shipping routes. This study provides theoretical and practical references for enhancing the resilience of Sino-Russian energy trade and optimizing global energy governance, with prospects for further interdisciplinary research integrating big data and micro-level case studies.
Read moreOPTION VALUE CALCULATION AFFECTED COMPONENTS
As the subprime credit crisis has attracted attention to financial derivative instruments, more frequently arises questions about fairvalue calculations. Over the time, different models had been introduced. All of those models take into account factors affectingprices. Mostly, factors used in calculations on the same type of financial instruments are approximately the same. Therefore questionarises, which factor affects price more and which less, with no matter which model would be used for fair value calculations. One offinancial derivative instrument types is options. Options are agreements, which give to option buyer rights to buy or sell underlyingasset. While the seller or writer of option has obligation to buy or sell underlying asset. This research aims to explore the impact offactors on option fair value calculations and evaluate most important ones from those, which could be chosen by option buyer orseller. To reach the aim of research following tasks are developed: 1) review of fair value calculation models; 2) compare results ofusage of different models and changes in affecting factors; 3) highlight differences between option price affecting factors, modelsused in calculations and results provided. Research includes literature review and analysis of option pricing results. Option pricecalculations are based on historical option prices, using black-Scholes and Binomial option pricing models. KEYWORDS: options, fair value models, strike price, exercise date. DOI: http://dx.doi.org/ 10.15181/rfds.v11i3.617
Read moreImpact of oil exports and non-oil exports on economic growth in Saudi Arabia: an econometric study using ARDL approach
This study’s primary goal is to examine Saudi Arabia’s performance from 2000 to 2022. In order to accomplish this, the Autoregressive Distributed Lag (ARDL) model was employed along with a limits test. The study’s findings indicate that oil exports impact short-term and long-term outcomes during the specified study period. On the other hand, non-oil exports initially contribute positively to the country’s domestic product in the short term, but this contribution diminishes quickly and becomes negative and statistically insignificant in the long term. As a result, Saudi Arabia is dependent on the export of a single commodity, making it vulnerable to the effects of market volatility on the price of oil. To escape the excessive dependence of Saudi Arabia on oil and encourage non-oil export activities in order to stimulate long-term economic growth, the research recommends expanding into other productive sectors, such as agriculture and industry. These two sectors are vital for economic diversification, to obtain improved growth, and to limit the ramifications of the negative effects caused by international changes in oil prices. It is essential to take this strategy to prevent excessive reliance on this one-of-a-kind resource, this diversification is crucial for promoting exports beyond hydrocarbons and reducing reliance on oil. improve its level of investment in its thriving domestic sectors and take steps to lower the country’s high production costs by constructing infrastructure that would enable the growth of non-oil exports, especially because Saudi Arabia will become a member of the BRICS group of countries beginning in January 2024.
Read moreModeling and Testing Volatility Spillovers in Oil and Financial Markets for the USA, the UK, and China
The main purpose of the paper is to analyze the conditional correlations, conditional covariances, and co-volatility spillovers between international crude oil and associated financial markets. The prices of oil and its interactions with financial markets make it possible to determine the associated prices of financial derivatives, such as carbon emission prices. The approach taken in the paper is different from others in the literature; the purpose is to examine the usefulness of modeling and testing volatility spillovers in the oil and financial markets. The paper investigates co-volatility spillovers (namely, the delayed effect of a returns shock in one physical or financial asset on the subsequent volatility or co-volatility in another physical or financial asset) between the oil and financial markets. The oil industry has four major regions, namely North Sea, the USA, Middle East, and South-East Asia. Associated with these regions are two major financial centers, namely the UK and the USA. For these reasons, the data to be used are the returns on alternative crude oil markets, returns on crude oil derivatives, specifically futures, and stock index returns in the UK and the USA. Given the importance of the Chinese financial and economic systems, the paper also analyzes Chinese financial markets, where the data are more recent. The USA and China are the world’s two largest economies and the UK is the world’s sixth largest economy (and second in the existing EU) behind the USA, China, Japan, Germany, and India. Moreover, the USA and the UK are associated with WTI and Brent oil, respectively. One of the purposes of the paper is to examine how China might be different from the USA and the UK, which seems to be borne out in the empirical analysis. Based on the conditional covariances to test the co-volatility spillovers, dynamic hedging strategies will be suggested to analyze market fluctuations in crude oil prices and associated financial markets.
Read moreHedging the Crack Spread during Periods of High Volatility in Oil Prices
Traditional approach to hedging crude oil refining margin (crack spread) adopts a fixed 3:2:1 ratio between the futures positions of crude oil, gasoline, and heating oil. However, hedging the latter in arbitrary proportions might be more effective under some conditions. The paper constructs optimal hedging strategies for both scenarios during the periods of relatively stable and volatile oil prices observed in recent years. Minimization of downside risk (LPM2) and variance are used as alternative hedging objectives. The joint distribution of spot and futures price shocks is modeled using a kernel copula method. The hedging performance of the constructed strategies is compared using hedging effectiveness, expected profit, and expected shortfall. Results show that allowing for arbitrary proportions in sizes of futures positions generally achieves better hedging performance. The advantage becomes particularly important during periods characterized by a high volatility of the cross-dependence between the prices of individual commodities. In addition, using ??????2 as a hedging criterion can help hedgers to better track downside risk as well as lead to higher expected profit and lower expected shortfall.
Read moreTHE IMPACT OF GLOBAL RISKS ON THE WORLD TRADE AND ECONOMIC ENVIRONMENT
It is noted that the unprecedented dynamic globalization of trade and economic relations and the fourth industrial revolution cardinally transform the global distribution system of the world economy, accompanied by the growing impact of global challenges and risks, the failure to take into account the effects of which permanently reduces the efficiency of economic functioning and international trade. For developing countries affected by geopolitical challenges, the development of partnerships with countries that are recognized as global leaders in the world economy is essential in terms of national interests and the promotion of state sovereignty.The purpose of this paper is to characterize the impact of global risks on the formation and implementation of trade and economic policies of countries based on the methodological approaches of leading international economic institutions and organizations. Major global risks have identified rising / falling prices for assets, oil or gas, changes in the structure of trade and economic cooperation, terrorism, separatism, climate change, unemployment, income inequality, proliferation of weapons of mass destruction, cyberattacks, etc.The following methods of scientific research were used to achieve the goal and to solve the tasks of the article: systematic structural analysis of economic processes and phenomena, method of quantitative and qualitative comparisons, tabular method of calculating the degree of influence.The scientific novelty of the results is to study the processes of formation and implementation of trade and economic policies of countries under the influence of exogenous factors on them. The influence of exogenous factors is characterized not only according to the sectoral classification (economic, geopolitical, technological, social and natural), but also taking into account the degree of influence of the factor (global challenges and global risks) on the environment.It is substantiated that in the conditions of globalization of the world economy, the threats receive a corresponding more serious nature. Therefore, government agencies need to develop new effective tools for their minimization in order to prevent negative effects and to implement more productive trade and economic cooperation with partner countries.
Read moreRetrofitting carbon capture and storage to natural gas-fired power plants: A real-options approach
Retrofitting carbon capture and storage to natural gas-fired power plants: A real-options approach